Let the displacement and force be approximately harmonic functions of \(\hat{t}\) , \(x(\hat{t})=a_x(\hat{t}) \sin {(\hat{\omega } \hat{t} + \phi _x(\hat{t}))}\)  and \(\hat{g}(\hat{t})=a_g(\hat{t})\sin {(\hat{\omega } \hat{t} +\phi _g(\hat{t}))}\)  respectively, with \(\hat{\omega }=\omega /\omega _0\) . The amplitudes and phases are assumed to vary slowly, at characteristic times much shorter than the inverse of the resonance frequency \(\omega _0\) . In the high \(Q\)  limit, the slow dynamics of the resonator can be modelled by applying the method of averaging [1]}, [2]}:
CCLL

ax=-ax - 12 ag  a
